R/utils.R

In sinib: Sum of Independent Non-Identical Binomial Random Variables

Defines functions q K Kp Kpp Kppp Kpppp saddlepoint

q=function(u,p){
	return(p*exp(u)/(1-p+p*exp(u)))
}
K=function(u,n,p){
	return(sum(n*log(1-p+p*exp(u))))
}
Kp=function(u,n,p){
	return(sum(n*q(u,p)))
}
Kpp=function(u,n,p){
	q_=q(u,p)
	return(sum(n*q_*(1-q_)))
}
Kppp=function(u,n,p){
	q_=q(u,p)
	return(sum(n*q_*(1-q_)*(1-2*q_)))
}
Kpppp=function(u,n,p){
	q_=q(u,p)
	return(sum(n*q_*(1-q_)*(1-6*q_*(1-q_))))
}
saddlepoint=function(u,n,p,s){
	return(Kp(u,n,p)-s)
}

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